rigify - add a Finger during animation
Once a rigify rig is created, it can be treated the same way as every other rig.

The armature modifier creates a relationship between a bone from the rig and a vertex group of the mesh with EXACTLY THE SAME NAME of the bone.

So: select your rig, go to edit mode, extrude E or divide W your finger bones until you're happy with the result, give to all modified bones a proper name, select the character, in the properties window - vertex tab - create new vertex groups with the same name of the new or modified bones, weight them manually using the "assign" button under the vertex group tab, and his relative value slider.
Assign "1.0" value of every vertex of the finger near to a bone, except near the junction: in those cases assign "0.5" value to both bones of the junction.

As tkausl said in the comments, you'll not loose any part of the already done animation, as soon as you do not modify the bones involved in your animation.

Also deleting unecessary bones from a rig is OK.